Is Aereo, a service that lets consumers stream over-the-air TV, akin to a cable company or a hardware provider like RadioShack? The justices of the Supreme Court appeared to struggle with that question on Tuesday morning as they listened to oral arguments in what many media watchers view as the most important TV-related court case in decades.

In deciding how to respond to broadcasters’ claim that Aereo is violating copyright, the court expressed repeated concern over how to write a ruling that did not create major ripples for the rest of the TV business on one hand, or for the cloud computing business on the other.

“It makes me nervous about taking your preferred route … Where does it stop?” said Justice Stephen Breyer, addressing Paul Clement, the lawyer for ABC and other big broadcasters that want to shut Aereo down.

Breyer and other Justices expressed particular concern about the broadcasters’ claim that they have a public performance right in Aereo’s transmissions, which are controlled by its subscribers. Breyer pointed out that a thousand people can — and do — store a file in a personal cloud service like Dropbox, and can play it back at the same time — which could be considered a public performance under the broadcasters’ version of the case.

The “public performance” question is the central issue in the closely-watched case, which turns on whether Aereo’s antenna technology, infringes broadcasters’ copyright, or if the service is instead an extension of existing legal services like remote DVR’s.

Chief Justice John Roberts also pressed Clement, noting that Aereo appears to provide an antenna in the same way that RadioShack does. But he also expressed deep skepticism over Aereo’s technology, asking why it rents out tens of thousands antennas rather than using just one.

“Is there any reason you need 10,000 of them?” asked Roberts, suggesting the only reason Aereo’s technology operates this way is to get around copyright laws.

“There’s no technically sound reason to use all those antennas,” added Justice Ruth Bader Ginsburg.

David Frederick, the lawyer for Aereo, responded by suggesting that modular designs help startups who don’t know how quickly they will have to scale up and that, in any case, efficiency questions are irrelevant for copyright purposes.

The justices also pressed Clement over how the court could square a ruling in the broadcasters’ favor with the decision in a case called Cablevision, in which an influential appeals court ruled that remote DVR’s are legal. The court noted that the Cablevision ruling was not binding on it, but that the outcome appeared correct. Clement responded by stating that the outcome in Cablevision was indeed correct, but that the lower courts’ reasoning for allowing remote DVR’s was all wrong.

For copyright watchers, the Justices’ questions left no clear indication of how the case will turn out. While Ginsburg appeared, as expected, to be clearly in the broadcasters’ camp, the other Justices expressed repeated concern over the cloud computing issue, and also expressed sympathy at times for one of Aereo’s central contentions — that the signals that are picked up by its customers’ antennas are local over-the-air transmissions that are free already.

Photo from Aereo

And, in a possible nod to an argument made in a supporting brief signed by 36 law professors, several justices suggested that what the case was really about was a reproduction right — not a public performance right. As Frederick was quick to point out, the broadcasters chose not to rely on the reproductive right argument because, had they done so, they would have run afoul of a seminal case 30 years ago that found private copying by VCR’s does not infringe copyright.

The case is significant not just for Aereo, which operates in 11 cities and is backed by media mogul Barry Diller, but for the entire TV industry. The broadcasters have warned that they may remove their over-the-air signals, and become cable channels if Aereo wins. Barry Diller, whose company IAC had put up most of the $97 million invested in Aereo so far, says the company is “finished” if the court grants the broadcasters an injunction.

Aereo released this transcription of a statement it delivered at the court following the hearing:

From our perspective, the issue in the case was whether consumers who have always had a right to have an antenna and a DVR in their home and make copies of local over-the-air broadcast television, if that right should be infringed at all simply by moving the antenna and DVR to the cloud.

The court’s decision today will have significant consequences for cloud computing. We’re confident, cautiously optimistic, based on the way the hearing went today that the Court understood that a person watching over-the-air broadcast television in his or her home is engaging in a private performance and not a public performance that would implicate the Copyright Act.

A decision is likely to come sometime in June or July. The case attracted considerable attention, including an overnight line for seats that began forming on Monday evening.